Uniformly Discrete Forests with Poor Visibility

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4 Scopus citations


We prove that there is a set F in the plane so that the distance between any two points of F is at least 1, and for any positive ϵ < 1, and every line segment in the plane of length at least ϵ-1-o(1), there is a point of F within distance ϵ of the segment. This is tight up to the o(1)-term in the exponent, improving earlierestimates of Peres, of Solomon and Weiss, and of Adiceam.

Original languageEnglish (US)
Pages (from-to)442-448
Number of pages7
JournalCombinatorics Probability and Computing
Issue number4
StatePublished - Jul 1 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics


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